Siqi Pan Intergenerational Risk Sharing and Redistribution under Unfunded Pension Systems. An Experimental Study. Research Master Thesis

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1 Siqi Pan Intergenerational Risk Sharing and Redistribution under Unfunded Pension Systems An Experimental Study Research Master Thesis

2 Intragenerational Risk Sharing and Redistribution under Unfunded Pension Systems: An Experimental Study Siqi Pan June 20, 2011 Abstract In the presence of idiosyncratic income risk and rate of return risk, does an unfunded pension play a role in intragenerational risk sharing? Towards its redistributive nature, what are the attitudes of high- and low-income earners respectively? How do people adjust their saving and risk management behaviors under dierent pension systems? As a result, how does a pension system aect the social welfare when taking into account the issue of risk exposure? This paper intends to answer these questions using an experimental method. Consistent with most theoretical predictions from the model, the main ndings are: (i) lowincome earners shows more support for unfunded pensions; (ii) when high-income earners take a larger proportion in a society, people of all income levels are more supportive for unfunded pensions; (iii) an unfunded pension discourages savings in funded pensions; (iv) people tend to take on more risk in their funded pensions as the unfunded pension expands; (v) low-income earners benet more from an unfunded pension; (vi) more risk averse agents benet more from an unfunded pension. 1 Introduction With demographic changes in most countries, discussion on state pension reforms has heated up in literature. 1 Due to decreasing birth rates while increasing longevity, if unfunded, pay-asyou-go (PAYG) public pensions continue to play a key role in retirement incomes, contribution rates will have to become substantially higher in order to balance the system. The problem I would like to thank Eline van der Heijden and Jan Potters, who supervised this thesis and provided great help in the whole process of my research. I am grateful for the valuable suggestions by Johannes Binswanger, and the excellent research assistance by Maolong Xu and Hengli Zhang. Financial support from Netspar is gratefully acknowledged. All remaining errors are mine. Department of Economics, Tilburg University, Tilburg, the Netherlands. S.Pan@uvt.nl 1 See, for example, Feldstein (1996)[4], Mitchell and Zeldes (1996)[11], Kotliko (1996)[10], Conesa and Krueger (1998)[3], and Sinn (1999)[14]. 1

3 here is whether the advantages of unfunded pensions worth the cost. Advocates of a switch away from PAYG schemes focus on the lower labor and capital market distortions and a higher level of private savings under funded systems. However, it has gone relatively unnoticed that redistributive public pensions constitute a risk sharing device against some kinds of uncertainty that could not be covered by personal pensions. This is especially important when the private insurance markets are incomplete, which has been well proved by such empirical studies as Hayashi et al. (1996)[7], Attanasio and Davis (1996)[1], etc. Therefore, it is crucial to understand possible adverse eects after replacing the unfunded system. If they turn out to be substantial, it might worth second thought before policy implementation. This study aims to investigate the issues of intragenerational risk sharing and redistribution under dierent pension systems in an experimental setting. If annuities are available, funded pensions are able to protect people perfectly against length of life risk. Hence mainly two other forms of risk are discussed here: idiosyncratic income risk and rate of return risk. Throughout I generalize funded pensions as exible private savings for retirement, that is, dened contribution personal portfolios consisting of assets with dierent levels of expected returns and risk exposure. Here I only consider bonds as riskless assets, and stocks as risky assets. It is mainly the risky part of a portfolio that generates rate of return risk in such pensions. Moreover, in a world where idiosyncratic labor incomes are not perfectly insurable, income shocks from working years will have an impact on contributions, thus having lasting eects upon pension benets. In contrast, unfunded pensions could give insurance against income risk and are hardly dependent on rate of return risk, especially in countries where the benets of PAYG systems are very imperfectly linked to contributions. The redistributive nature (from high-income earners to low-income earners) is the reason why some kinds of risk are big for individuals, but are aggregated out over the society. Due to the dierences in risk management mechanism between funded and unfunded pensions, people of dierent income levels would give various responses to the change of pension systems. It remains controversial whether a fully funded pension system would benet agents of all income levels when taking the issue of risk exposure into consideration, which is strongly dependent on how people behave under various circumstances. However, surprisingly few comparisons have been made in a micro scope, either on behavioral changes under dierent pension systems, or on preference dierences between high- and low-income earners. Hence, this paper intends to address the following questions: (1) What are the attitudes of people on dierent income levels towards the scale of an unfunded pension, especially regarding its redistributive nature? Will such attitudes change in societies with dierent wealth distribution? 2

4 (2) What is the eect of an unfunded pension on people's saving behaviors? (3) As the unfunded part expands in a pension system, how do people adjust the risk management in their funded pension portfolios? Are there any dierences in such behaviors for agents with dierent risk attitudes? (4) Which pension system can bring about the highest social welfare? For agents of each income level with dierent risk attitudes, what are the pros and cons of a certain pension system? To bring out the issues in a stark way, here I assume: (i) contribution to funded pensions and portfolio allocation are exible; (ii) unfunded pensions are highly redistributive and have no risk; (iii) bonds earn the same risk-free rate of return as the PAYG scheme, which is given by the growth rate of aggregate wage income; (iv) agents face borrowing constraints; (v) the economy is in steady states where both demographic structure and wealth distribution are unchanging and pension schemes are in balance; (vi) each generation expects that the current pension policy would last for at least one generation. Now I give some justications for these assumptions. In practice, unfunded pensions do have risk in most countries. Nevertheless, they provide a large scale of redistribution in many developed countries, such as the UK, Canada, the Netherlands, etc. As a consequence, the reduction in risk exposure to negative earnings shocks could also be very substantial. 2 The returns of bonds are not constant over time either. However, according to Binswanger (2007)[2], the expected returns of bonds and PAYG schemes are close and both variances are considerably lower than that of stocks. 3 Assumptions (v) and (vi) make it possible to isolate individual decisions from an overlapping generations framework, which greatly simplies experiment implementation. The laboratory environment allows us to obtain detailed information on individual behaviors and to isolate the marginal eects of key determinants, thus answering the research questions above. The experiment is set in an economy where coexist two types of individuals: rich and poor. Each can live for two periods: the working period and the retirement period. The working wage in period 1 is exogenous and could be interpreted as current wealth accumulation. The retirement income in period 2 is stochastic and could be interpreted as one's future income. Compared to the poor type, a rich agent has a higher working wage as well as a higher expected retirement income. The pension system is composed of a funded and an unfunded part. It becomes fully funded when the unfunded part is zero. The funded pension could be invested in a portfolio consisting of bonds and stocks. Bonds earn a constant rate of return, which is the same as that of the unfunded pension. Stocks earn a stochastic rate of return with a higher expected value. The unfunded part is a compulsory PAYG scheme that levies a tax on working 2 For details see Gruber and Wise (1999)[6] 3 See Table 2 of Binswanger (2007)[2], where the reported gures refer to returns simulated over 32 years from 1929 to 2003 (adjustment made for the two-period model). 3

5 wages and gives an identical benet after retirement. The experiment is conducted in a unit of three-person group. Based on the combination of types in their groups, subjects are rstly required to vote for the tax rate, which reects the scale of the unfunded part. The median number becomes the eective tax rate. Then, faced with the income risk after retirement and the rate of return risk on stocks, subjects decide how to allocate savings and smooth consumption over two periods. The voting, saving and risk taking behaviors are of interest in this paper. Most theoretical predictions regarding such behaviors are well supported by experimental results, which lead to the following conclusions: (1) compared to high-income earners, low-income earners shows more support for unfunded pensions; (2) people are more supportive for unfunded pensions in a society where high-income earners take a larger proportion; (3) an unfunded part in the pension system discourages funded pension savings; (4) those who are more risk averse tend to choose less risky portfolios; (5) people tend to take on more risk in their funded pensions as the unfunded part expands in the pension system; (6) an unfunded part leads to lower returns and smaller risk exposure in the pension system for a society as a whole; (7) compared to high-income earners, low-income earners benet more from an unfunded pension; (8) compared to risk neutral agents, those who are more risk averse benet more from an unfunded pension. The rest of the paper is organized as follows. Section 2 introduces the theoretical model and experimental design. In Section 3, I give theoretical predictions simulated from the model and then formulate hypotheses. Experimental procedures are described in Section 4 and experimental results are reported in Section 5. Section 6 concludes. All instructions are included in Appendix A and Appendix B. 2 Model and design Throughout I base the discussion on a two-period model, which is a simplication of the three-period overlapping generations (OLG) model by Samuelson (1958)[12]. This section rst introduces these two models, based on which the experimental design is described in detail. 2.1 A three-period OLG model Consider an economy populated by overlapping generations. Each generation lives for three periods. Agents work and earn wages in the rst two periods, whereas in period 3, they retire and earn nothing. Denoting consumption of an agent in the j th period by C j (j =1, 2, 3), his/her utility is then U = U(C 1, C 2, C 3 ). Now suppose a generation consisting of N agents, who are in the rst period of their lives. Each of them has earned a wage w 1 in period 1, which is exogenous and could also be interpreted as current wealth accumulation. The wage in period 2 is w 2, which is stochastic (the tilde indicates uncertainty) and could also be interpreted as one's 4

6 future income. The expected value of w 2 conditional on w 1 (E[ w 2 w 1 ]) is positively correlated with w 1, that is, those who have had a higher wage in the past will have a better chance to earn more in the future. Period 3 is the retirement period and no one receives any income. Figure 1: A three-period OLG model Agents smooth their consumption through a pension system composed of a funded and an unfunded part. The funded part takes the form of private savings denoted by S 1 in period 1 and S 2 in period 2, which earn a rate of return R after every period. The unfunded part levies a tax at the rate t on working wages in period 1 and 2, and gives a benet P in period 3. As a PAYG scheme, the unfunded pension has a structure illustrated in Figure 1. For each generation, pension benets are contributed by the next generation (indicated by the subscript +1) through tax payment. Now I assume: (i) the unfunded pension earns a riskless rate of return R b, which is given by the growth rate of aggregate wage income; (ii) the economy is in a steady state, where the demographic structure and the income distribution are unchanging. Therefore, we have N +1 = N, w 1,+1 = R b w 1, E[ w 2,+1 ] = R b E[ w 2 ], where E[ ] denotes the mathematical expectation operator, and w 1 is the income per capita in period 1. Hence, the balance of the unfunded pension is given by P = R b(t N +1 w 1,+1 ) + t N +1 E[ w 2,+1 w 1,+1 ] N = R b(tn +1 w 1,+1 ) + tn +1 E[ w 2,+1 ] N = tr 2 bw 1 + tr b E[ w 2 ] In this way, the second assumption frees us from the OLG framework. 5

7 2.2 A two-period model Since one of the main issues of this study is the idiosyncratic income risk embodied in w 2, only the saving decision in period 1 is of interest here. Hence, the original framework can be simplied to a two-period model (see Figure 2), in which period 3 is removed and period 2 is set as the retirement period. Figure 2: A two-period model The utility of an agent i is thus given by U i = U(C 1,i, C 2,i ). In period 1, he/she earns a working wage w 1,i, pays a tax at the rate t, and saves into a funded pension account. In period 2, he/she has a retirement income w 2,i, pays a tax at the rate t, gets returns from the funded pension account, and receives a benet P from the unfunded pension scheme. Again, E[ w 2,i w 1,i ] is positively correlated with w 1,i. Since now the benet P is received in period 2 rather than period 3, the balance of the unfunded pension becomes (discounted by R b ) P = t(r b w 1 + E[ w 2 ]) Notice that P is the same for everyone in the economy. Hence the benets are imperfectly linked to contributions, which endows the unfunded pension with properties of redistribution and risk sharing. As we can see, this two-period model is able to display both properties and still to capture income uncertainty. 4 Now I introduce another risk into the model: the rate of return risk. The funded pension could be invested in a portfolio of assets consisting of bonds 4 It is easy to see that the unfunded pension is now a combination of a PAYG scheme and a social security system. The PAYG scheme taxes on working wages of the next generation and redistributes among the current retired generation. The social security system taxes on retirement incomes and redistributes within the retired generation. Although the interpretation is dierent, it plays the same role here as the pure PAYG scheme in the three-period model. 6

8 and stocks. Bonds earn a constant rate of return R b, which is the same as that of the unfunded pension. Stocks earn a stochastic rate of return R k, which has an expected value larger than R b (E[ R k ] > R b ). Hence, for an agent i who allocates B i into bonds and K i into stocks, the consumption in period 1 is the after-tax working wage minus savings in the funded pension; the consumption in period 2 is the after-tax retirement income plus returns from the funded pension, and the benet from the unfunded pension, that is, C 1,i = (1 t)w 1,i B i K i C 2,i = (1 t) w 2,i + R b B i + R k,i K i + P Since C 2,i depends on the outcome of uncertainty in future income and rate of return, it is also a random variable. The nal payo is given by the product of consumptions in both periods. Since for each agent, working wage w 1,i is set to be considerably larger than expected retirement income E[ w 2,i w 1,i ], the multiplicative form provides strong incentive for consumption smoothing. To set forth the risk management issue in a relatively simple way, here I use a utility function of the mean-variance form following Shiller (1999)[13]: U i = E[C 1,i C 2,i ] γ i 2 Var[C 1,i C 2,i ] where γ i is the risk aversion parameter of agent i. A larger value of γ i means a higher degree of risk aversion. Hence, under a given pension system, the decision problem for an agent i is to choose the optimal B i and K i so as to maximize his/her utility, in the face of two independent shocks: an idiosyncratic income shock on w 2,i and a rate of return shock on R k,i. Also, in the experimental design, the pension system, specically, the tax rate is determined via a voting process, which will be described in Section 2.3. To depict saving behavior, I dene saving rate s i as the proportion of working wage invested in one's funded pension; to depict risk-taking behavior, I dene the risk management ratio λ i as the weight of stocks in one's funded pension portfolio, that is, s i = K i + B i w 1,i, λ i = K i K i + B i 2.3 Experimental design Based on the two-period model above, the experiment is conducted in a unit of three-person group. Each round of decision making involves a voting process and two periods. In the voting process, each group member votes for a tax rate. Such a process results in an eective unfunded pension, thus an eective pension system. Then the experiment proceeds to period 1, when each 7

9 agent makes an independent decision on saving and risk management, given the pension system in practice. After that, outcomes of two risks on future income and rate of return, as well as the nal payo are revealed for each agent in period Types, states and a voting process In the economy, there coexist two types of agents: rich and poor. Types dier with respect to incomes. For a rich agent i, the working wage w 1,i = 12, while the retirement income follows the 4, Prob = 1 2 4, Prob = 1 4 distribution: w 2,i =. For a poor agent i, w 1,i = 8 and w 2,i =. 0, Prob = 1 2 0, Prob = 3 4 Hence, the rich type has a higher wage in period 1, as well as a better chance to earn a high retirement income in period 2. Also, there are two possible states of three-person groups: good and bad. When a group is formed by two rich agents and one poor agent, such a state is called good. When a group is formed by one rich agent and two poor agents, such a state is called bad. Due to dierent income distribution in two states, as far as the unfunded pension is concerned, the mapping for each tax rate t to the benet P is also dierent. If I assume R b = 1, then the relationship between t and P is given by P = t in a good state, whereas P = 3 t in a bad state.5 At the beginning, each agent is informed of his/her own type and the state of his/her group. Then starts the voting process. Every group member casts a vote in the form of a percentage chosen from the set {0%, 10%, 20%, 30%, 40%, 50%}. The median percentage becomes the eective tax rate. Since the median voting mechanism makes sincere voting a (weakly) dominant strategy, the vote that an agent casts serves as a measure of his/her preference for the scale of the unfunded part in the pension system Saving and risk management The voting process determines an unfunded pension for each group, which levies a tax at the rate t on the incomes of all group members in both periods, and gives an identical benet to everyone in period 2. Besides, a funded pension account is provided as well. Savings in such an account could be allocated into two kinds of assets: bonds B i with a constant rate of return R b = 1, and stocks K i with a stochastic rate of return following the distribution: 2, Prob = 1 2 R k,i =. 1 2, Prob = 1 2 For both types, the working wage is considerably larger than the expected retirement income, and the nal payo is given by the product of consumptions in both periods. Therefore, there is strong incentive for consumption smoothing by means of the pension system. Hence, under an 5 In a good state, P = t(r b w 1 + E[ w 2 ]) = t( ) = t; in a bad state, P = t(r bw 1 + E[ w 2 ]) = t( ) = t. 8

10 unfunded pension scheme determined by voting, each agent needs to decide on a funded pension portfolio, that is, to choose values for B i and K i. The two variables of interest here are s i and λ i, which reect the saving and risk management behavior respectively. 3 Predictions and hypotheses This section gives theoretical predictions based on the two-period model and experimental design, and then formulates hypotheses accordingly. By assuming various risk attitudes of agents (γ = 0, 0.05, 0.1, 0.2, 0.3), optimal behaviors are simulated for every possible combination of type and state (called scenario hereafter), thus providing an overall picture of the main determinants of voting, saving and risk-taking behavior. 3.1 Voting behavior The optimal tax rate of an agent depends on his/her trade-o between the redistributive and risk sharing nature of an unfunded pension. Apparently, redistribution makes an unfunded pension more favorable for poor agents, while the risk sharing eect makes it more desirable for risk averse agents. Therefore, both income level and risk preference should be taken into account while voting for the pension system. Table 1 summarizes the best votes of agents with ve dierent values of risk aversion parameter in every scenario, which provides the following predictions. Table 1: Optimal votes by type, state and risk preference State Good Bad Type Rich Poor Rich Poor γ= γ= γ= γ= γ= (i) When the group is in a good state, a rich agent with a relatively low degree of risk aversion (for example, when γ = 0 or 0.05) tends to vote for a fully funded pension system. For such an agent, the loss from redistribution of an unfunded part is larger than the gain from its risk sharing eect. However, a more risk averse agent benets more from risk sharing. Hence, in either state, the optimal tax rates of the rich type are positively correlated with γ. (ii) Redistribution provides great benets for the poor in a good state. As a result, despite the fact that stocks in the funded part earn a higher expected rate of return than the unfunded 9

11 part (E[ R k ] > R b ), it is still optimal to vote for 50% even for a risk neutral poor agent. (iii) Compared to the good state, the same tax rate t in a bad state is corresponding to a smaller benet P. Therefore, for some values of γ (for example, when γ = 0.05 or 0.1), the best votes of the rich type in a bad state are lower than those in a good state. (iv) Again, in a bad state, the unfunded pension gives a smaller benet for a certain tax rate. As a consequence, although the poor will benet from redistribution, those who are less risk averse would prefer to smooth consumption via stocks rather than an unfunded pension (because E[ R k ] > R b ). Hence, in a bad state, the best votes of a poor agent might be lower than 0.5, and they are positively correlated with γ. (v) For some values of γ in either state, the best votes of a rich agent are lower than those of a poor agent. From the analysis above, a hypothesis concerning voting behavior could be formalized as follows. Hypothesis 1 (on vote) (a) Between types: in either state, compared to rich agents with the same average degree of risk aversion, poor agents vote for higher tax rates on average; (b) between states: on average, both rich and poor agents vote for higher tax rates in a good state; (c) with risk preference: more risk averse agents vote for higher tax rates. 3.2 Saving behavior Figure 3: Saving rates and tax rates One of the most important justications for a funded pension is that such a policy could produce an equivalent increase in national savings, thus reducing the burden placed on the future workers who must support the retired elderly under an unfunded system. This argument 10

12 is clearly supported by Figure 3, which shows a strong negative correlation between tax rates and the optimal saving rates predicted by the model, holding others constant. Moreover, the marginal eect is inuenced by risk preference and changes slightly in dierent scenarios. 6 Hence, the following hypothesis concerning saving behavior is formulated. Hypothesis 2 (on saving rate) Saving rates are negatively correlated with tax rates, that is, savings in the funded pension decrease as the unfunded pension expands. 3.3 Risk management Figure 4: Risk management and risk preference When it comes to risk management behavior, it is straightforward that when other conditions are the same, less risk averse agents tend to allocate more savings into stocks, which is supported by the negative correlation between λ and γ shown in Figure 4. 7 Such a relationship seems quadratic and the marginal eect is inuenced by tax rate, type and state. Another important relationship is between λ and t. As displayed in Figure 5, when controlling for other factors, agents take on more risk in funded pension portfolios with an increase in tax rate (except for risk neutral agents, λ does not change). By setting, the unfunded pension earns a lower expected rate of return than stocks. Therefore, as the unfunded pension expands, agents choose portfolios with a larger weight of stocks to increase expected returns. Again, when γ > 0, the correlation seems quadratic and the marginal eect is aected by risk preference, type and state. Hence, I have the following hypothesis with respect to risk-taking behavior. 6 Figures are similar when γ =0.05, 0.1 or Figures are similar in the other two scenarios 11

13 Figure 5: Risk management and tax rates Hypothesis 3 (on risk management ratio) (a) With risk preference: λ is negatively correlated with γ, that is, those who are more risk averse tend to choose less risky portfolios; (b) with tax rate: λ is positively correlated with t, that is, as the scale of the unfunded pension increases, agents take on more risk in their funded pension portfolios. 3.4 Welfare I rst focus on the welfare of the entire group. Its relationship with the pension system is closely related to the risk sharing eect of the unfunded part. By setting, an unfunded pension leads to lower returns and smaller risk exposure. Hence, when the tax rate increases, both mean and variance of payos declines. According to the mean-variance utility function used in the model, for those who are risk neutral (γ = 0), welfare depends only on the mean, but not the variance of payos. In this case, a larger unfunded part will decrease the average utility (see the dotted line in the left part of Figure 6). However, when group members are more risk averse, the average welfare might become positively correlated with tax rates (see the dotted line in the right part of Figure 6). This is because such a group will gain more utility from risk sharing. 12

14 Now I separately discuss the welfare of each type concerning the issue of redistribution. Figure 6 displays the correlation between welfare and tax rates in each scenario. In a group with γ = 0 (see the left part of Figure 6), risk sharing does nothing to improve utilities. Hence, as the tax rate increases, rich agents are subjected to losses not only from lower expected payos, but also from redistribution. For poor agents, on the other hand, the eect is a trade-o between gains from redistribution and losses from lower expected payos. Gains exceed losses in a good state, yet can hardly oset losses in a bad state. However, the conclusion might be dierent for a group with a higher degree of risk aversion, where risk sharing plays a more important role in utility improvement. In this case of γ = 0.3 (see the right part of Figure 6), both types in either state will gain from an expanding unfunded pension. The increase in welfare is larger for poor agents than for rich agents due to the redistributive eect. Now we can formalize the following hypothesis regarding people's welfare. Figure 6: Utility by type, state and risk preference Hypothesis 4 (on welfare) (a) For a group as a whole, both mean and variance of payos are negatively correlated with tax rates, that is, an unfunded part would lead to lower returns and smaller risk exposure in the pension system; (b) compared to rich agents, poor agents would benet more from an unfunded pension, holding others constant; (c) controlling for other aspects, those who are more risk averse would benet more from an unfunded pension. 4 Experimental procedures The experiment was conducted in four sessions at Tilburg University. Eighteen students participated in each session, for a total of 72 subjects. No subject participated in more than one 13

15 session. The experiment was computerized and the scripts were programmed using the z-tree platform (Fischbacher, 2007[5]). All sessions used an identical protocol. Upon arrival, subjects were randomly seated behind computer terminals, which were separated by partitions. The experimenter distributed written instructions (see Appendix A) and announced that everyone had received the same copy. Then subjects were given plenty of time to read instructions and ask questions. To check their understanding of the instructions, they had to give correct answers to four questions before the rst formal round began. The main experiment (Experiment 1) ended after the 30th round. Then all subjects were requested to participate in a lottery experiment (Experiment 2) designed to assess their risk preferences. Again, subjects received written instructions (see Appendix B) and had plenty of time to read. They were informed that the instructions were the same for everyone, and the two experiments were completely independent. After nishing the lottery experiment, subjects were paid privately via bank transfer. The nal payment was the sum of payos in both experiments, plus a show-up fee of 5. All sessions lasted for about one and a half hours and subjects earned an average of 14.4 (with a minimum of 8.8 and a maximum of 20.1). 4.1 The main experiment This experiment used points as experimental currency units, with an exchange rate of 150 points to 1 Euro. At the beginning of each session, subjects were randomly given a type as rich or poor, which they retained throughout the session. Experiment 1 consisted of 30 rounds of decision making. Each round proceeded under identical rules and consisted of a voting process and two periods. The experiment, mainly the voting process, was conducted in a unit of three subjects called group. Half of the groups were in a good state (formed by 2 rich subjects and 1 poor subject), whereas the other half were in a bad state (formed by 1 rich subject and 2 poor subjects). Groups were randomly rematched and states were randomly decided at the beginning of each round. Before voting, subjects were informed of the state of their own group, yet their identities were never revealed. After the voting process, each group reached an eective pension system, under which every subject was asked to make an independent decision on saving and risk management, specically, to allocate their funded pension savings into bonds and stocks. Then the experiment proceeded to Period 2, when each subject observed his/her own realization of two risks on future income and rate of return, and the payo for the current round was displayed and a new round started. 4.2 The lottery experiment After Experiment 1, subjects were required to complete a short lottery experiment. The 14

16 design was a variation of Holt and Laury (2002)[8], where subjects chose between a xed payo and an all or nothing lottery. There were 11 pairs of choices dierent in values of the xed payo (increased from 0 to 4 in steps of 0.4). The lottery could pay either 4 or 0 with an equal probability 50%, and it remained the same for all pairs. The switch point serves as an ordinal measure of risk attitudes. 8 A random incentive system was used to determine payos. That is, one out of 11 pairs was randomly chosen for actual payment. 5 Results Experimental results are reported in this section. After giving descriptive statics of some key variables, I discuss voting, saving and risk-taking behaviors in dierent scenarios. To analyze the main determinants of such behaviors, some regression results are presented as well. In the end, welfare of rich and poor subjects under dierent pension systems is compared in terms of returns and risk exposure. 5.1 Descriptive statistics Table 2: Mean, standard deviation, minimum and maximum of key variables Mean Std. Dev. Min Max # Obs. vote t B K s λ a RA payof f a 88 observations of λ were dropped due to zero divisors. Throughout I take into account all of the decisions made by all subjects during the experiment, which gives a balanced panel data with 72 individuals and 30 time periods. The mean, standard deviation, minimum and maximum of some key variables are summarized in Table 2. Among them, vote 0, 0.1, 0.2, 0.3, 0.4, 0.5 is the tax rate that a subject vote for during the voting process. As dened in the model, t 0, 0.1, 0.2, 0.3, 0.4, 0.5 is the tax rate in practice, that is, the voting result of a group; B and K are the amounts of bonds and stocks in one's funded pension; s [0, 1] is the saving rate dened as the proportion of working wage invested in the funded pension; λ [0, 1] is the the risk management ratio dened as the weight of stocks 8 The switch point equals one plus the number of times that a subject chose the lottery before switching to the safe choice. 15

17 in one's funded pension portfolio; payoff is the amount of points received in a round. RA is a measure of risk attitude from the lottery experiment. Let x be one's switch point from the risky lottery to the safe choice. Then RA = 12 x. 9 Table 3: Mean (and standard deviation) of key variables by session Session 1 Session 2 Session 3 Session 4 vote 0.21(0.20) 0.14(0.19) 0.19(0.20) 0.19(0.20) t 0.20(1.16) 0.09(0.13) 0.18(0.16) 0.16(0.16) B 1.59(1.94) 1.45(1.61) 1.15(1.36) 1.28(1.35) K 1.71(1.43) 2.82(1.74) 1.80(1.43) 2.18(1.48) s 0.33(0.18) 0.43(0.15) 0.29(0.15) 0.35(0.19) λ 0.55(0.36) 0.66(0.33) 0.65(0.35) 0.65(0.31) RA 5.61(1.46) 5.33(1.38) 5.22(1.62) 6.00(1.45) Payo 31.80(19.65) 34.74(22.96) 35.38(19.35) 32.78(21.48) # Obs. a a 88 observations of λ were dropped due to zero divisors. Table 3 describes these key variables on a session level. Comparing means and standard deviations across sessions, we could see some dierences, which implies the possible necessity to include session dummies as regressors in estimation. 5.2 Voting behavior The histograms in Figure 7 provide evidences for the rst two statements in Hypothesis 1. For rich subjects, the average vote (and standard deviation) is 0.10(0.16) in a good state, and 0.07(0.14) in a bad state. For poor subjects, the average vote (and standard deviation) is 0.31(0.19) in a good state, and 0.26(0.19) in a bad state. 10 The Mann-Whitney U test between each two scenarios is signicant at 1%. Hence, by comparing votes between types in the same state, the rst statement in Hypothesis 1 is supported: poor subjects vote for higher tax rates than rich subjects in either state. By comparing votes between states within the same type, the second statement is supported: both rich and poor subjects vote higher in a good state. To analyze the determinants of voting behavior, three specications of a random-eect Tobit model are estimated and the results are reported in Table 4. Here the dependent variable vote is treated as continuous. Out of 2160 observations, 915 (42.36%) are subject to left-censoring at the value 0, whereas 386 (17.87%) are subject to right-censoring at the value 0.5. Due to the 9 Please notice that RA could not be compared in value with the parameter γ in the model. 10 There is no signicant change in RA for dierent scenarios. Therefore, here the degree of risk aversion could be seen as controlled at its average level

18 large amount of observations at the censoring values, I use the Tobit model for estimation. And due to the need to observe time-invariant variables such as type and risk attitude, the random eect method is chosen over the xed eect. 11 Figure 7: Vote distribution by type and state The specication in column (1) includes only key determinants such as risk preference, type and state. An interaction term between type and state is also included to examine whether the eect of state is dierent for two types. The unobserved heterogeneity captures half of the variance not explained by regressors (ρ = 0.50), which indicates the importance of individual eects. Since the data exhibit some variances on a session level (as shown in Table 3), the second specication includes three dummy variables to examine session eects. However, these session dummies are jointly insignicant (F-test, p-value=0.74), and the inclusion of them as regressors does not bring any signicant improvement to the original model. Therefore, there seems no need to include them into the model. 11 In all of the regressions below, the estimation of time-variant variables does not change signicantly when using the xed eect method. 17

19 Table 4: Estimation results on vote (1) (2) (3) RE Tobit 1 RE Tobit 2 RE Tobit 3 RA (0.03) (0.03) (0.03) Rich -0.52(0.09)*** -0.52(0.08)*** -0.42(0.09)*** Good 0.10(0.02)*** 0.10(0.02)*** 0.10(0.02)*** Rich Good -0.05(0.03) -0.05(0.03) -0.04(0.03) Session (0.11) Session (0.12) Session (0.12) Round (0.0009) Rich Round -0.01(0.002)*** Constant 0.28(0.16)* 0.30(0.19) 0.29(0.16)* ρ Log-likelihood # obs Note: Rich is a dummy that takes value 1 for the rich type. Good is a dummy that takes value 1 if the group is in a good state. Session i is the dummy variable for session i (i=1, 2, 3). Round indicates round number. Multiplication sign ( ) means an interaction term between the variables before and after. Standard errors in parentheses. ()* signicant at 10%; ()** signicant at 5%; ()*** signicant at 1%. In each scenario, taking the average vote in each round as one observation, we can observe whether there is a pattern of voting behavior across rounds. Figure 8 shows a decreasing trend in the average vote of rich subjects over time, whereas the trend is not so clear for poor subjects. Moreover, the volatility seems decrease from round to round. These might suggest a learning process of subjects. To control for the above-mentioned eects, the third specication includes the variable Round and the interaction term between round and type. The estimation results are in line with the gure. The coecient of Round implies no signicant change in poor type's voting behavior over time. However, by taking the interaction term into consideration, we can conclude that the average vote of rich subjects exhibits a signicant decreasing trend over time. These two variables are jointly signicantly dierent from zero (F-test, p-value<0.01), and the inclusion of them brings some improvement to the original model. Hence, I base my further discussion on the specication in column (3). Here I typically calculate marginal eects in the last round (Round=30) for a subject with the probability of voting between 0 and 0.5 equal to When the group is in a bad state (Good=0), compared to the poor type and holding others constant, votes of the rich type are lower by on average. Such a dierence increases to when the group is in a good state. Also, compared to a bad state while holding others unchanged, poor subjects in a good state 12 As explained in Honore (2008)[9], the parameter estimates for both random eect and xed eect models can be converted to marginal eects by multiplying them by the fraction of observations that are not censored. HerePr(0 < vote < 0.5 X it, α i ) = ( )/ , where X it is the vector of explanatory variables and α i is the unobservable individual heterogeneity. 18

20 vote higher by 0.04 and rich subjects vote higher by on average. These further support the rst two statements of Hypothesis 1. However, since the coecient of RA is insignicant and considerably small in value, we nd no evidence for the third statement concerning risk preference. This might suggest that during the voting process, subjects put most attention on the redistributive rather than the risk sharing property of the unfunded pension. Figure 8: Trend of average vote by type and state 5.3 Saving behavior After the voting process, decisions on saving and risk management are made independently by each subject. The voting results, that is, the eective tax rates of the unfunded pension can be seen as treatments. From the distribution of tax rate in Table 5, we can see the number of observations under fully funded pension (t = 0) is 768, while the number of observations under unfunded pension (t > 0) is Now I rst focus on subjects' saving behaviors. Table 5: Number of observations (and percentage) in the distribution of tax rate by state State Good Bad Good/Bad t = 0 456(42.22%) 312(28.89%) 768(35.56%) t = (21.39%) 183(16.94%) 414(19.17%) t = (18.33%) 222(20.56%) 420(19.44%) t = (6.11%) 180(16.67%) 246(11.39%) t = (5.00%) 87(8.06%) 141(6.53%) t = (6.94%) 96(8.89%) 171(7.92%) Total 1080(100%) 1080(100%) 2160(100%) 19

21 Saving rate s, the dependent variable here, is a continuous variable between 0 and 1. Out of 2160 observations, 88 (4.07%) are subject to left-censoring, and only 13 (0.6%) are subject to right-censoring. Since only a small number of observations are at limit, I use a RE model to simplify the discussion. The regression results of three specications are reported in Table 6. In column (1), only key determinants are included. The unobserved heterogeneity captures 45% of the variance not explained by regressors, which indicates the importance of individual eects. Then four interaction terms between type, state, risk preference and tax rate are included in the second specication. They are jointly signicant (F-test, p-value<0.01) and make slight dierences in the estimated results. The estimation in column (3) takes session and time period eects into consideration. Both a joint F-test of three session dummies (p-value=0.04) and a t-test of the variable Round (p-value<0.1) are signicant. Hence I use the third model for further analysis. Table 6: Estimation results on saving rate (1) (2) (3) RE 1 RE 2 RE 3 t -0.59(0.02)*** -0.60(0.07)*** -0.62(0.07)*** RA 0.004(0.01) 0.005(0.01) 0.004(0.01) Rich -0.02(0.02) -0.03(0.03) -0.03(0.02) Good 0.03(0.01)*** 0.04(0.01)*** 0.04(0.01)*** Rich Good -0.02(0.01) -0.04(0.01)*** -0.04(0.01)*** Rich t 0.05(0.05) 0.05(0.05) Good t -0.11(0.05)*** -0.12(0.05)*** Rich Good t 0.17(0.06)*** 0.17(0.06)*** RA t (0.01) (0.01) Session (0.03) Session (0.03) Session (0.03) Round (0.0003)*** Constant 0.42(0.05)*** 0.42(0.05)*** 0.47(0.05)*** ρ # obs Note: Rich is a dummy that takes value 1 for the rich type. Good is a dummy that takes value 1 if the group is in a good state. Session i is the dummy variable for session i (i=1, 2, 3). Round indicates round number. Multiplication sign ( ) means an interaction term between the variables before and after. Standard errors in parentheses. ()* signicant at 10%; ()** signicant at 5%; ()*** signicant at 1%. As we can see, the estimated results give a good support for Hypothesis 2. For a poor subject with the average degree of risk aversion (RA = 5.54), the marginal eect on saving rate of an 20

22 increase in tax rate by 10% is -6.3% in a bad state, and -7.5% in a good state. If the subject is rich, the marginal eect is -5.8% in a bad state, and -5.3% in a good state. Therefore, it is clear that an unfunded part in the pension system discourages personal savings. 5.4 Risk management By denition, here the dependent variable λ is a continuous variable between 0 and 1. Out of 2072 observations, 114 (5.50%) are subject to left-censoring, and 715 (34.51%) are subject to right-censoring. 13 Therefore, a RE Tobit model is used for estimation, and the results of four specications are reported in Table 7. Table 7: Estimation results on risk management ratio (1) (2) (3) (4) RE Tobit 1 RE Tobit 2 RE Tobit 3 RE Tobit 4 t 0.36(0.06)*** -0.23(0.17) 1.86(0.82)*** 2.01(0.85)** t (0.38)*** -1.04(1.57) -1.11(1.69) RA -0.04(0.03) -0.03(0.13) 0.05(0.14) 0.05(0.14) RA (0.01) -0.01(0.01) -0.01(0.01) Rich 0.06(0.11) 0.05(0.11) 0.06(0.11) 0.07(0.11) Good -0.06(0.02)** -0.06(0.02)*** -0.06(0.02)*** -0.04(0.04) Rich Good 0.08(0.03)** 0.08(0.03)** 0.07(0.03)** 0.08(0.06) RA t -0.67(0.23)*** -0.65(0.23)*** RA t (0.27) 0.39(0.27) t RA (0.02)*** 0.05(0.02)*** Rich t 0.28(0.49) Rich t (1.07) Good t -0.52(0.49) Good t (1.15) Rich Good t -0.35(0.68) Rich Good t (1.55) Constant 0.87(0.21)*** 0.90(0.35)*** 0.70(0.36)** 0.68(0.36)*** ρ Log-likelihood # obs Note: Rich is a dummy that takes value 1 for the rich type. Good is a dummy that takes value 1 if the group is in a good state. Multiplication sign ( ) means an interaction term between the variables before and after. Standard errors in parentheses. ()* signicant at 10%; ()** signicant at 5%; ()*** signicant at 1%. Mainly two relationships of λ are predicted by the model: its negative correlation with RA, and its positive correlation with t. According to the theoretical prediction, both two relationships seems quadratic (see Figure 4 and Figure 5). But rstly, a basic linear model is estimated in column (1). The unobserved heterogeneity captures more than a half of the variance not observations of λ were dropped due to zero divisors. 21

23 explained by regressors (ρ = 0.63), which indicates the importance of individual eects. To examine quadratic relationships, then the squared terms for tax rate and risk aversion t 2 and RA 2 are included in column (2), and the interaction terms between t and RA, t 2 and RA, t and RA 2 are included in column (3). Both specications improve the original model and the added terms are jointly signicant (F-test, p-value<0.01). The specication in column (4) adds more interaction terms between type, state and tax rate into the model. It does not bring about signicant improvement and the added terms are jointly insignicant (F-test, p-value=0.20). Therefore, to simplify the model, I choose the third specication for analysis. 14 The marginal eects are calculated for a subject whose value of λ is between 0 and 1 with probability Suppose both tax rate and degree of risk aversion are at the average level (t = 0.16, RA = 5.54). Then the marginal eect of every unit of increase in RA on risk management ratioλ is -4.1%. Although the coecients of RA and RA 2 are not signicant, given the range of RA is from 0 to 9, this eect is not very small in value and the sign is in line with the theoretical prediction: those who are more risk averse tend to choose less risky portfolios. For an increase in tax rate by 10%, the marginal eect on λ is 5.7%. 16 This indicates that subjects tend to take on more risk in their funded pensions when the unfunded part expands in the pension system. Therefore, both statements in Hypothesis 3 are supported by experimental data. 5.5 Welfare Table 8: Average payo (and standard deviation) by state and type State Good Bad Good/Bad Type Rich Poor Rich Poor Rich/Poor t = (25.10) 19.80(11.34) 53.62(24.20) 20.06(11.23) 37.35(25.58) t = (19.99) 21.93(9.61) 48.13(21.68) 22.20(10.25) 35.91(21.01) t = (15.27) 21.85(9.42) 41.27(19.22) 20.47(8.50) 32.00(17.50) t = (16.06) 21.94(7.26) 40.91(11.30) 20.38(7.07) 29.34(14.47) t = (17.35) 23.62(7.01) 36.18(12.79) 21.61(6.79) 28.72(13.60) t = (13.85) 23.28(7.20) 27.68(14.93) 19.89(5.83) 26.20(12.42) # obs According to the utility function in the model, subjects' welfare under dierent pension systems should be discussed with respect to both mean and variance of payos. As long as subjects are responsive to the treatment of tax rate, the rst statement of Hypothesis 4 should 14 The inclusion of session dummies and the time period variable does not make much dierence (F-test, p- value=0.19). 15 Pr(0 < λ < 1 X it, α i ) = ( )/ , where X it is the vector of explanatory variables and α i is the unobservable individual heterogeneity. 16 This eect is negative when tax rate is 0 or 0.1, which suggests that subjects' risk management behavior is not quite responsive when the tax rate is low. 22

24 be true by setting, that is, an unfunded part would lead to lower returns and smaller risk exposure in the pension system for a group as a whole. Such a claim is well supported by the results in the last column of Table 8. Now I analyze the welfare of each type separately. For the rich type, both mean and variance of payos in either state decrease as the tax rates increases. Hence, an unfunded part would lead to losses for rich subjects who are risk neutral. From the data reported in Table 8, we are able to calculate the benchmark value of risk aversion parameter according to the model. If a subject has a risk aversion parameter larger than such a benchmark, he/she would be better o under an unfunded pension of a certain scale, compared to a fully funded pension where t = 0. For example, when t = 0.4, the benchmark value is for rich agents in a good state, that is, rich agents with γ > would benet from this unfunded pension. The benchmark increases to in a bad state, where benets of the unfunded pension are lower. For the poor type in a good state, as the unfunded part expands, the average payo increases while the volatility decreases. This implies that poor agents benet from an unfunded pension in terms of both redistribution and risk sharing. In a bad state, there is still decrease in the variance, yet the increase in the mean is not so clear. This conrms the prediction that in a bad state, an unfunded part will not benet poor agents who are risk neutral, but will benet those who are more risk averse (see Table 1). Hence, the analysis above proves the second and the third statement of Hypothesis 4: compared to rich agents, poor agents benet more from an unfunded pension; compared to risk neutral subjects, those who are more risk averse benet more from an unfunded pension. 6 Conclusion While considering a switch away from an unfunded pension system, it is crucial to understand the role it is playing in the economy other than consumption smoothing. This paper focus its discussion on the issues of intragenerational risk sharing and redistribution. An experimental method is used to observe people's voting, saving and risk taking behaviors. Most theoretical predictions regarding such behaviors are well supported by experimental results, from which we could draw the following conclusions: (1) compared to high-income earners, low-income earners shows more support for unfunded pensions; (2) people are more supportive for unfunded pensions when the society is in a good state; (3) an unfunded part in the pension system discourages funded pension savings; (4) those who are more risk averse tend to choose less risky portfolios; (5) people tend to take on more risk in their funded pensions as the unfunded part expands; (6) an unfunded part leads to lower returns and smaller risk exposure in the pension 23

25 system; (7) compared to high-income earners, low-income earners benet more from an unfunded pension; (8) compared to risk neutral agents, those who are more risk averse benet more from an unfunded pension. These conclusions provide us some policy implications regarding the choice between funded or unfunded pensions. It is clearly seen from the experimental results that subjects are able to realize both redistributive and risk sharing natures of unfunded pensions. However, redistribution is the major concern during the voting process. The remarkable distinction in voting behaviors between high- and low-income earners suggests that the sustainability of an unfunded pension depends heavily on wealth as well as power distribution of a society. The positive eect of funded pensions on private savings is well proved by the results. However, the risk sharing eect of unfunded pensions are also quite clear. Hence, during the transition from unfunded to funded pension systems, it is very important to accelerate the development of private insurance markets so as to cover the increasing risk exposure. On the other hand, since people tend to choose more risky portfolios as the unfunded pension expands, the issue of rate of return risk is still noteworthy even under unfunded pension systems. 24

26 Appendix A. Instructions for Experiment 1 The currency used in this experiment is point. The experiment consists of 30 separate rounds. In each round, you will have the opportunity to earn a certain amount of points. After 30 rounds, the points you have earned will be added up and converted into Euros at the rate of 150 points to 1 Euro. Your payment in Euros for this experiment will thus be equal to your payoff in points divided by 150 (rounded). 1. Your Role Each participant plays a role (Role A or Role B) throughout this experiment. The assignment of roles is randomly determined by the computer. Your role stays the same from round to round. 2. Your Payoff (in points) Each round consists of a voting process for a Policy, and two periods: Period 1 and Period 2. We first describe how the amount of points earned in each round is determined. You receive an amount of points at the beginning of each period, called Start Asset. After a series of activities, the amount of points you own at the end of each period is called End Asset. The product of the End Asset of Period 1 and the End Asset of Period 2 determines your payoff for that round. Therefore, if we denote the Start Asset of Period 1 and of Period 2 as and respectively, and the End Asset of Period 1 and of Period 2 as and respectively, then your payoff for the round is given by points. See Table 1. Table 1: Payoff for the Round Period Period 1 Period 2 Start Asset End Asset Payoff for the Round 3. End Asset Your End Asset of Period 1 and of Period 2 are determined by the Start Asset of each period, the Policy decided by voting, your saving decisions, and returns of your saving accounts Start Asset In Period 1, Role A receives a Start Asset of 12, whereas Role B receives 8. In Period 2, the Start Asset is determined randomly. It could be equal to 4 or 0. Role A receives 4 with probability 50% or 0 with probability 50% (the expected value is 4 50% 0 50% 2). Role B receives 4 with probability 25% or 0 with probability 75% (the expected value is 4 25% 0 75% 1). See Figure 1. 25

27 For Role A For Role B Start 1 = 12 Start 1 = 8 Start 2 = 0 4 Start 2 = % 50% 50% 75% Figure 1: Start Assets for Role A and Role B 3.2. The Policy There is a Policy that collects a tax of the rate on the Start Assets in both Period 1 and Period 2, and gives a fixed amount of benefits in Period 2. Therefore, under such a Policy, you have to pay in Period 1 and in Period 2 as taxes, so you can receive in Period 2. The after-tax Start Asset of Period 1 is 1. The after-tax Start Asset of Period 2 is Saving Accounts You make two saving decisions in Period 1. These two decisions only affect the payoff of your own, but NOT the payoffs of other participants. From your after-tax Start Asset of Period 1 ( 1 ), you decide how and how much to save for Period 2. Two saving accounts are provided: Bond and Stock. Suppose you decide to save points into the Bond account, and to save points into the Stock account. Then the rest of the after-tax Start Asset of Period 1 is your End Asset of Period 1. That is, 1 After the decision making in Period 1, you enter Period 2. The points in the Bond account do NOT change, that is, the returns of the Bond account in Period 2 are equal to your savings in Period 1. However, the amount in the Stock account could either decrease to a half or increase to double, with equal probability. That is, if you have saved into the Stock account in Period 1, returns of the Stock account may equal 0.5 or 2 in Period 2. Each case happens with probability 50%. See Figure 2 (next page). In Period I: B In Period II: Bank Account In Period I: K In Period II: Stock Account B 100% 0.5K 50% 2K 50% Figure 2: Returns of the Bond and the Stock Account 26

28 Your End Asset of Period 2 is the sum of the after-tax Start Asset of Period 2 ( 1 ), returns of the Bond account ( ), returns of the Stock account (0.5 2 ), and benefits of the policy ( ), that is, Your Start Asset of Period 2 (4 or 0) and returns of the Stock account (2 or 0.5 ) are randomly determined by the computer. You do NOT make any decision in Period 2. The descriptions above are summarized in Table 2 below. Table 2: Start Asset and End Asset Period Role Period 1 Period 2 Start Asset A 4 % 0 % B 4 % 0 % End Asset A&B % 2 50% Payoff for the Round A&B 4. Voting for the Policy Now we describe how the tax rate and benefits of the Policy are decided. The Policy (the tax rate and its corresponding benefits ) is determined by a voting process by each group in each round. At the beginning of each round, you are randomly matched with 2 other participants and form a Group of 3 members. The Policy is decided by the votes of all the 3 group members. The voting result is only valid for members of your own group and lasts for only one round. Decisions in all other groups are irrelevant to your group. The group formation also lasts for only one round. When a new round starts, a new group of you forms randomly, and a new Policy is decided by voting. Each group member cast a vote in the form of a percentage (%) chosen from the set {0, 10, 20, 30, 40, 50}. After that, you are informed of the voting result of your group. However, your decision is anonymous. That is, no participant learns about the voting decisions of the others. The voting result is the median percentage. For example, if in a group, the votes of the three members are 20%, 0%, 40% respectively, then the result equals the median number 20%. The median number is obtained by two steps. We firstly order the three percentages from small to large: 0%, 20%, 40%; then the number in the middle is the median number, that is, the value of. 27

29 As a result of the voting, each group member has to pay a fraction from the Start Assets of both periods as taxes, and receives an identical and fixed amount of benefits in Period 2. Therefore, the tax payments might be different for each group member (depending on the values of and ), but the benefits are the same for every member. The value of benefits is equal to the expected tax revenues divided by 3. Now we explain this in detail. We already know that for Role A, the Start Asset of Period 1 and of Period 2 are 4 50% 0 50% So Role A s expected Start Asset of Period 2 is: 4 50% 0 50%. For Role B, the Start Asset of Period 1 and of Period 2 are 4 25% 0 75% So Role B s expected Start Asset of Period 2 is: 4 25% 0 75%. There are two possible combinations of roles in a group. If there are 2 members in Role A and 1 member in Role B in a group (called Group A+A+B), then the benefits are given by If there are 1 member in Role A and 2 members in Role B in a group (called Group A+B+B), then the benefits are given by Please notice that the benefit level is ONLY related to the tax rate decided by voting ( ). It is NOT impacted by the realized value of (4 or 0) or the realized returns of the Stock Account (0.5 2 ) for any group members. Therefore, the relationship between the voting result and the corresponding benefit level is the same for a given combination of group (A+A+B or A+B+B), which is calculated in Table 3. Table 3: Tax Rate and Benefits (rounded) of the Policy Group 0% 10% 20% 30% 40% 50% A+A+B A+B+B Table 4 summarizes the taxes and benefits under different policies in Group A+A+B. For example, suppose the voting result is 20%. For Role A, in Period 1, the tax payment is 12 20% 2.4; in Period 2, the tax payment may equal 4 20% 0.8 with probability 50%, or equal 0 with probability 50%. For Role B, in Period 1, the tax payment is 8 20% 1.6; in Period 2, the tax payment may equal 4 20% 0.8 with probability 25%, or equal 0 with probability 75%. Both Role A and Role B receive the same benefits % 2.5 in Period 2. 28

30 Table 4: Taxes and Benefits of the Policy in Group A+A+B Role A in Group A+A+B Role B in Group A+A+B Taxes Benefits Taxes Benefits Period 1 Period 2 0% 10% 20% 30% 40% 50% 0% 10% 20% 30% 40% 50% or 0 or 0 or 0 or 0 or 0 0% 10% 20% 30% 40% 50% % 10% 20% 30% 40% 50% 0% 10% 20% 30% 40% 50% or 0 or 0 or 0 or 0 or 0 0% 10% 20% 30% 40% 50% Table 5 summarizes the taxes and benefits under different policies in Group A+B+B. Continue the example of 20%. In Group A+B+B, tax payments for Role A and Role B are the same as Group A+A+B. However, now both Role A and Role B receive the same benefits % 2.1 in Period 2. Table 5: Taxes and Benefits of the Policy in Group A+B+B Role A in Group A+B+B Role B in Group A+B+B Taxes Benefits Taxes Benefits Period 1 Period 2 0% 10% 20% 30% 40% 50% 0% 10% 20% 30% 40% 50% or 0 or 0 or 0 or 0 or 0 0% 10% 20% 30% 40% 50% % 10% 20% 30% 40% 50% 0% 10% 20% 30% 40% 50% or 0 or 0 or 0 or 0 or 0 0% 10% 20% 30% 40% 50% The Procedure Now we describe how a round proceeds. Each round begins with a voting process displayed in the following screen (next page). On the top you can see your role (stays the same throughout the entire experiment), and the combination of your group for this round. You are requested to vote on the policy for your own group. After inputting a number from the set {0, 10, 20, 30, 40, 50}, press the Confirm button to see the voting result of your group. 29

31 Your Role. Your Group. Input your vote. Press to proceed. Then Period 1 begins. You will see the following screen, in which you are asked to input your savings in the Bond account ( ), and savings in the Stock account ( ). Both are accurate to the first decimal place (0.1). Press Confirm to proceed after decision making. Input B. Input K. Press to proceed. Then Period 2 begins. In the following screen, you are informed of the realized value of your Start Asset of Period 2, realized returns of the Bond and the Stock account, and benefits from the Policy. Your End Asset of Period 2 is calculated. Start Asset of Period 2: 4 or 0. Returns of Stock Account: 0..5 K or 2 K. At the end of each round, you will see a record screen summarizing your choices and payoff in the current round, and the accumulated payoff for all the rounds before. 30

32 6. Summary Experiment 1 consists of 30 separate rounds. Your final payoff for this experiment is the sum of your payoffs in all the 30 rounds. Every round is composed of a voting process and two periods. You receive a Start Asset in each period. Your payoff for that round is the product of the End Asset of Period 1 and of Period 2. You play a role (Role A or Role B) throughout the experiment. In each round, you are randomly matched with 2 other participants to form a Group (Group A+A+B or Group A+B+B). The 3 group members vote on the tax rate of a Policy. The result is the median percentage. Then every group member pays a fraction of the Start Assets in both periods, and receives an identical benefit in Period 2 (The relationship between taxes and benefits are summarized in Table 4 and Table 5). Therefore, for Role A, Role A: Period 1 Period 2 Policy: Savings: Start Asset: - Tax: - Savings into Bond Account: - Savings into Stock Account: Start Asset: 4 % 0 % - Tax: = End Asset: = End Asset: Payoff for the Round: + Benefits of the Policy: + Returns of Bond Account: % + Returns of Stock Account: 2 50% In Period 1, Role A s End Asset ( ) is calculated as: Start Asset of 12, minus tax payment, minus savings in the Bond account, minus savings in the Stock account. In Period 2, the End Asset ( ) is calculated as: the Start Asset, which equals 4 with probability 50% or 0 with probability 50%, minus tax payment, plus benefits of the Policy, plus returns of the Bond account, plus returns of the Stock account, which could be 0.5 or 2 with equal probability. The roles differ with respect to Start Assets. Compared to Role A, the only two differences for Role B are: (i) the Start Asset of Period 1 is 8, NOT 12; (ii) the Start Asset of Period 2 equals 4 with probability 25% or 0 with probability 75%, NOT 4 with probability 50% or 0 with probability 50%. All the rest conditions are the same. Therefore, for Role B, Role B: Period 1 Period 2 Start Asset: Start Asset: 4 % 0 % Policy: - Tax: - Tax: + Benefits of the Policy: - Savings into Bond Account: + Returns of Bond Account: Savings: % - Savings into Stock Account: + Returns of Stock Account: 2 50% = End Asset: = End Asset: Payoff for the Round: 31

33 Instructions for Experiment 2 Now we begin the second experiment. You will be presented with 11 pairs of options on your computer screen. In each pair, you are asked to choose between Option A: a fixed payoff that you get for sure; Option B: an all or nothing lottery, where with probability 50% you win 4 and with probability 50% you win nothing. To determine your payoff in the lottery (Option B), the computer randomly draw a number between 1 and 100. If the number is less than or equal to 50, you get 4. If the number is greater than 50, you get 0. Once you have made all the 11 choices, the computer will randomly select one out of these 11 pairs for real payment. The lottery in Option B is the same in all pairs. Only the safe payoff in Option A increases from pair to pair. Now consider the fifth pair of options, Pair 5. Suppose you chose Option A. You would receive 1.6 for sure. Suppose you chose Option B. If the randomly drawn number were less than or equal to 50, you would receive 4. If the randomly drawn number were greater than 50, you would receive 0. Please choose the option you most prefer for all the 11 pairs. Press the Confirm button when you finish. Then the results will be displayed on the screen. 32